A non-perturbative framework for N-point functions of locally non-Gaussian fields

Abstract

We present a non-perturbative approach to correlation functions and polyspectra of locally non-Gaussian fields and develop a semi-perturbative framework that does not rely on a local expansion. This enables the computation of $N$-point functions of non-Gaussian fields even when the mapping between the auxiliary Gaussian field $ζ_{\rm G}$ and the non-Gaussian field $ζ({\bf x}) = F(ζ_{\rm G}({\bf x}))$ is non-analytic. As an example, we consider non-Gaussian fields with exponentially tailed distributions, which can arise, for instance, in ultra-slow-roll models of inflation, and derive some exact analytic results in the strongly non-Gaussian regime.